Research of Application the Virtual Reality Technology in Chemistry Education

Size: px
Start display at page:

Download "Research of Application the Virtual Reality Technology in Chemistry Education"

Transcription

1 Journal of the Korean Chemical Society Printed in the Republic of Korea * ( ) Research of Application the Virtual Reality Technology in Chemistry Education Jong Seok Park*, Kew Cheol Shim, Hyun Sup Kim, Jaehyun Kim, Hai Il Ryu, and Young Chul Park Institute of Science Education, Kongju National University, , Korea (Received August 29, 2002).!" #!$ %&. ' () * +!, -. / #!6 78 9&. :;6 +/ <4= -A /B C DE #. F,G /08 HI!$ %&. J" KL, MN, OP Q RS,T UV1 W1 X YZ [\$ %&. () ]^ I_L`,Ta YZ b cd Ief 7g1 hi\$ %&. I_L`,j IN b (ka `El _mn &. :;! +/ o HIEp, -A d I_L` Eqrs* #!$ %gt, u v d,w xy. AI zn\{$, ` ` }~ * %&$ $\{&. w 6 d I_L`,j } A $ƒ! &. : ]^, I_L`, `El _mn, I_L` Eqrs, d ABSTRACT. As the computer is popularized in individual and society, it is using in a many of area. In particular, there are many materials to learn a science knowledge using multimedia through computer. Many of them are web-based learning materials, which are developed by Java or Flash. Since the technology of the representation, storage, computation and communication in computer make progress, the environment of education is also developed. Especially, the internet and VR technology will cause the education to change. A key feature of VR is real-time interactivity, in that the computer is able to detect student input and instantaneously modify the virtual world. It is reported that using the VR simulation in chemistry education can increase student engagement in class, promote understanding of basic chemical principles, and augment laboratory experience. In this study, application way of the virtual reality technology in chemistry education is examined. Keywords: Internet, VR, Real-Time Interactivity, VR Simulation, Chemistry Education 21,6 d # ˆ6 [,!,6 Š 7&. uœ1 Ž. ] 4 D #!, -. (computer literacy). E a '!&. L šp Q œ$ RS ž 6 Ÿ G I " z \$ %&.., ]^ F /0 1 }!, -. [I z\$ %&. u, +/" Ž. 6 ª. ` &. 450

2 a `[ _«&. ` *!6 7 g1!&.. LN 6 & ] # E &1 ]. N, l, ` 0, +/ ~ ± [ ²g1 ]A ` * `E!, ŠX ³ 9 &. a ±[ Av %6 9µ, u '!1 3 ¹ I_L`,j* } %&. G g1 I_L`º ]l %6 l #Ÿ* 1 L!$, 78 _mn * R! `[=»¼ %6 I_ O 4.&.. 1 ]YZ, I_ O, #½ ¾ ²g1 KL\6 I_L`(VR: Virtual Reality)a ] l Iz,T* À! 8Á I_ O 6 I  I_ l* L`à %" ÄÅ6 7ˆ $ Æ %&. I_L`a ]l l ] 2 ¾ (interface) ÇOI W1ÈÉg1Ê Uš\ l &. I_L`,j UV ËÌ x] Í Î g1 MÏAz Ð. 3 ¹ Ñ_ ÒÓ, Q. ]Ô cd1 ]A #½ l Õ Ð A >?* Ö" \{&. I_L` E 3 ]la L` O= O Ø A ÃÙ ] ÚÛ* RA _mn %&. ÜÝ Þ VRa 3 ¹ udß ¼ àî á Q â ã, ä 6 på1 [ %6 Ñ_ E * RA iæ!,6! I_L`* I %" Aç&. 4 6 &è A `[ _«&.!6 7 ' é Ì!$ LN6 N, l, ` Kw, ê ~ ² L` ±[ ë±!6 7 ì&.. ±[³8a 3 ¹ I_L`,j* }. E * RA íî %&. 5., I_L`,ja,œ. -+ ¹Ó L* -. : YZ* [A ï %gt, ð. + YZ* [!$ +/ <4= o, _ mn * ñ %, ë±, ò1uó 6 xu 1 IÍ ñ&. w 6 d I_L`* } %6 * ôõ$/ I_ d>* [n!$. ê8 Gö* â#! d I_L `,j } IÍ W1X 1 I_L `,j } IÍ *! &. 451 I_L`,j } a I_ ` ` ` * R. +/ <4 U Q `[ ` g1 ]A U ø %6 ±[³ :d, _ ] ¹Ó Þ. A Hz, ¹ù[ ` * R. N, l, ` 0 Q - [ú= a 9a N³8 * I $ %&. `[1 :; 3 ¹ I_L`,j 4 * }. E g1 L _«I û$ %6 N ±[, l ±[, ` Kw ±[, +/ ~ ±[ ²* AvA ž$ %&. 5 ü, I_l 4 \ %6 ý / 0 }!$ 2Ó þz ÿ Ç\ %6 `,, ¹ù[!t, I_l L`Ã* :.g 1. I_L` 3 ¹ ò1uó* } %&. I_L`,j* }. #1 Imprint Interactive Technology( &' o/= ÈÜ * é!6 I_YZ*! &. u '!1 ¹/ O(Atom world) 8 %6 x! &à &. ¹/ O +/6 ¹/ 8 ¹/ â X&. +/6 /, ' /, š/ a,w ¼ / A,K_ ¹/8* Â&. u8a io RA ¹/ 8 %&. n -= ¹ / å6 Ñ*!6 io6 òrg1 [ E\{&(Fig. 1, 2).. I_L`,ja ]l ]¾, `[ O= ú \ 6 l 4 I L\6 3 ¹ ] ò1uó [n* IÍ!"!, ë± YZ*!6 [ *, %* 7& /I ~ ] _mn * ég1ê + _«!t Gö %&. 7 õi, W1X j xu &. x U* R. /0 & d, %* 7&. d >! I_L`,j* }. /0 [n!$, ê8" Z!". I _L`,j* }. /0. u8 Gö* â#.&.

3 452! Fig. 2. Spin Indicator: The frame around the spinning electron is an active interface element. One end of the frame is a golden arrow, which indicates the direction of the electron s spin. The electron s spin direction can be changed by grabbing the golden arrow and moving it to point in the opposite polar direction. Students are required to change the spin direction for the second electron placed in each orbital shell. ( Fig. 1. Symbols for the atomic particles: protons (3-D plus signs), neutrons (cubes) and electrons (minus signs)(above). Power Bar: puts required energy into the system enabling the addition of electrons. Settings on the power bar indicate the various orbital levels: S1, S2, P1(below). ( I_L`* L %6 ò6 OpenGL, VRML, VRT, WorldToolKit ² %&. w / 0 xu!, -A #. 6 Ñ Superscape # 3D Webmaster&. 10l I_L` [n xu. Z * Bg 1 Superscape#I xu. 3D Webmaster6 _,, iæ " ² 3D F# å6 ò &. 7a Fä Q F ¾ [n!6  8" iâ1x 2D F¾ _mn IÍ. 3D I_ F¾ % =t, X [n YZ, è xu, &. ˆÓ [, VRML my, xu å(world) M ² ( k*!&.. = VCA " 100 I A #õ å [n E # %$, I_ å " _mn I %6 Ð. SCL(Superscape Control Language)* é!$ %&. 5! "# $% & Ñ Superscape # 3D Webmaster ò1uó*! d ž é$ #½ >* [n! &. #½ > d ž a /8 d ž ' I_L`,jg1 %!&$ hi., K, Ëå ` ²&. A ê8 + %. u8 Gö* DZg1 â#! &. DZ _a Ñ & ê g1 ' 2 25'(( 14, 11)&. DZ*!, š ê8",k= Ëå αpº ` A / ) Ç'!$, &à #½ >* Z! "! &. DZa 8x ±) A Ó* + 1 ö,!"! &. 8x ±) ' 4x6 I_L`. G DZ$, 4x6 d ž. DZ&. Ç ±a /8 xu!$ -!.! &. '( #) I_L`,jg1 [n. #½ >6 Journal of the Korean Chemical Society

4 [ šeÿ* >/ %$, šeÿ* 0 n~e 1 2 % _mn Þg1 \ %&( science.kongju.ac.kr/). ()!, 3 ` * ]^* RA ` A 2 %6 ¹ù[ ` >* 4! 5~ +>, Ó >, 6 7 >, Ÿ 8 >, ê' ]l>, >, YZ>,,T ±'>, + /0>g1 9e %&. d ž é\ %6 Ÿ8 >6 5I :7I % ê8a 8 :7 æy! + %&. u ',K= Ëå α. Pº ` ² ž * &à &.,K d6 ;< õd 4x ½= %&. 8 ÙÙa š,à, >d7, ¹/G?, œ,d 8, +/8 š,à ½ =* A š,à, EÙd! üe B&. ê8a RA,K, 8 * ÙÙ <4C" + %&. &è d xy8 = a Ôg1 +* %&. D, K _ Ù ¹ EF! ¹ UG/, 8, â ² d Ô &è dg1 [E\ +* %&. Fig. 3a >d7 ½=* HI* ë, K cd BÁ&.. Ëå α. Pº` a uj #zg1 Z K L{M i³* íî!$, I_L`,j N³] _mn Ô* ) }! +/8 `[1 ` *!6 7ÒN ÄO %gt 4E O >ƒ % [E\ %&(Fig. 4). d è< õd6 α¼/ P %6 ½= % ÙÙ!Q* A α¼/i RS* ÎA TõI 0z Q Pº L_* " $&. ½= ' I 453 Fig. 4. Scattering of the a-ray( N è<a œ,d n *!" $&. 8x DZ ±) Ù٠DZ A Ó* + 1 ö,. ê8 UVWa Table 1 &. š g1 ê8a I_L`,j* }. RA +!6 7 A X g1,$ %gt, (ê8&6 ê8 YË X { tz v 4. 6 B [&. I_L`. G ž DZ ê8a I_L` ` Þg1 +!6 7 \&$,t,. uj Ç' 8* ë& + ž * A!6 ] $&$ êù! &..^ I_L` ` Þ* &96 Š]* _ 6 &$ ö,! &. G, X ]Ô IN `a 7 a I_` Þ* & `!6 7& +!6 á & ˆ6 ±)&. 7 Fig. 3. Periodicity of the ionization energy(

5 454! Table 1. Response of students about the VRT-based chemistry program General item about VR Specific item about chemistry Item Mean Male Female Total It is a pleasure to learn through the VR experiment or model It is more understandable to learn through the VR experiment or model than through the picture or explanation. It is easy to handle the VR experiment or model It is more effective to learn through the VR experiment or model than through direct experiment For Rutherford experiment, the VR experiment is more understandable than a lecture The VR Rutherford Experiment is interesting For the periodicity of elements, using VR periodic table is more understandable than the text-based periodic table The VR periodic table is interesting a 0 `!6 7 ' * ae.&$ % &. ±) ê8a (ê8& &. v ê8a W1X + 1 I_L`,j* }. /0 A X, `[1 0 ] ` ' * (ê8& Ë '!" ]!$ %6 7&. d ž. DZ ê8a )b X {&.,K Ëå Pº` A Ç' /0 RA +!6 7&6 I_L `,j* }. /0 RA +!6 7 <4= A ñ %6 7g1 ö,\{&..^. I_L` /0 <4= á a /0 _ [ cˆ & 7g1 dz&. d 0 ] ` e '. 7 Lµ, ` g1 &9, 3 ž -. ` 8a I_L`,j* } A + /01 }.& ê8" A= <4 ñ * %* 7g1 dz&. 21, Ôf d E Ž. d * - A6 d YZ* d #. E g1 šye1!t, # %6 d ò1uó xu!&. = a YZ g1 I_L`,j* }. [n* 8 %&. I_L`,j6 W g!å= ò 1!, ë± í g1 }! h!$ %6 ` RS,T UV éi.!å= ò Iù ³ MÏA $ % jg1 } IÍ a ñ&$ %&. 5., I_L` 6 : Ða I_L` E [!6 kr &. &è 234 5! œ, \6 9 I _L` E [!6 &è N³8* $Š.& a b ±[I \ * 7&. õi I_L` E,l ` ` &è ³a d, ŸÓ, ² ~E ¹ %&6 ³&.. I_L`,j* d } ég1ê I 6 N³a I I %6 u ' I ú! mn, +/8 _mn Q E o RA /, +* %&. pn, 3 ¹ I_L`,ja,l 2 ¹ & +/ &. ÃÙ,>* /í!, ë± +/8 <4 U ] ø %&. qn, $I N #!ú - ña `. ¹ù [ ` ` XÑ I Í!&. ^n, I_YZ # /l `El _mn IÍ!, ë± +/ ~ üe GÑø %gt, E o RA r Av %&. 8 = a N³8a L $ %6 ±[³8 * AvA 6 g1 hi$&. cˆ I_L`,j* }! d > [n.& +/8 d + b ] ø 7g1 dz&. 9a +/8 ŠÈA A L6 îs! $ _ ] ž A &ÃÙ»¼ I_L`(Multisensory Immersive Virtual Reality),j á g1 Journal of the Korean Chemical Society

6 455 } ø %&6 v t, I_L`, & á g1 I_L`,j* d 9 ja +/I Ô*!6. YZ %* 7&. / O. Z 0>* Þ!6 %&.., I_L` } a +/1 ±a Tz< i!r + [ `.»¼Ã* HIE1 ~! ¹\{à(KRF D00075).,= o HEu %&..^, I_L`a W1X + Z * z!6! *.&. I_L`a EÙ, vùa Ÿ Ù* RA Ã!!, ë± / / L_ A» ¼! + Z *!.&. uœ1, I_L` a ìú _ ] Þ, à L6 L_ 6 Þd. ] * L!6 Ž!&. uó$ +/8 ` * R. +g1 Ô* Í~ g1!$ u Ô* w!$!t Gd!6 + á &. õi I_L` ^d $ 6 I_L` Mn +/" xé g1ê /S I_ O Ox, yz, ò1uó{, Z ² io ú g1 ê %* 7&. I_L`,j.,w N³8a d }!6 '. I ø %&., ` [1 +/8 I_L` A }. >³* I $ %gt, d ž ' ~ 7* I_L`1 LA!6 A YË? %6!" \ 1. Riva, G. PRESENCE. 1999, 8(4), Beier, K. P Walser, R. Chapter 4. In Helsel, S. K.; Roth, J. P. Virtual Reality: Theory, Practice and Promise (. 4N. :.. ;, 1994). 4. ; ; ; ; ;. 2001, 21(4) !"#.. $ %&: ', Jonassen, D. H. Educational Technology. 1994, Traub, D. Chapter 11. In Helsel, S. K.; Roth, J. P. Virtual Reality: Theory, Practice and Promise (. 4(. :.. :, 1994). 8. ; ; pp Dede, C.; Sazman, M.; Loftin, R. ScienceSpace/absvir.html

An Example file... log.txt

An Example file... log.txt # ' ' Start of fie & %$ " 1 - : 5? ;., B - ( * * B - ( * * F I / 0. )- +, * ( ) 8 8 7 /. 6 )- +, 5 5 3 2( 7 7 +, 6 6 9( 3 5( ) 7-0 +, => - +< ( ) )- +, 7 / +, 5 9 (. 6 )- 0 * D>. C )- +, (A :, C 0 )- +,

More information

! " # $! % & '! , ) ( + - (. ) ( ) * + / 0 1 2 3 0 / 4 5 / 6 0 ; 8 7 < = 7 > 8 7 8 9 : Œ Š ž P P h ˆ Š ˆ Œ ˆ Š ˆ Ž Ž Ý Ü Ý Ü Ý Ž Ý ê ç è ± ¹ ¼ ¹ ä ± ¹ w ç ¹ è ¼ è Œ ¹ ± ¹ è ¹ è ä ç w ¹ ã ¼ ¹ ä ¹ ¼ ¹ ±

More information

Vectors. Teaching Learning Point. Ç, where OP. l m n

Vectors. Teaching Learning Point. Ç, where OP. l m n Vectors 9 Teaching Learning Point l A quantity that has magnitude as well as direction is called is called a vector. l A directed line segment represents a vector and is denoted y AB Å or a Æ. l Position

More information

Planning for Reactive Behaviors in Hide and Seek

Planning for Reactive Behaviors in Hide and Seek University of Pennsylvania ScholarlyCommons Center for Human Modeling and Simulation Department of Computer & Information Science May 1995 Planning for Reactive Behaviors in Hide and Seek Michael B. Moore

More information

LA PRISE DE CALAIS. çoys, çoys, har - dis. çoys, dis. tons, mantz, tons, Gas. c est. à ce. C est à ce. coup, c est à ce

LA PRISE DE CALAIS. çoys, çoys, har - dis. çoys, dis. tons, mantz, tons, Gas. c est. à ce. C est à ce. coup, c est à ce > ƒ? @ Z [ \ _ ' µ `. l 1 2 3 z Æ Ñ 6 = Ð l sl (~131 1606) rn % & +, l r s s, r 7 nr ss r r s s s, r s, r! " # $ s s ( ) r * s, / 0 s, r 4 r r 9;: < 10 r mnz, rz, r ns, 1 s ; j;k ns, q r s { } ~ l r mnz,

More information

Framework for functional tree simulation applied to 'golden delicious' apple trees

Framework for functional tree simulation applied to 'golden delicious' apple trees Purdue University Purdue e-pubs Open Access Theses Theses and Dissertations Spring 2015 Framework for functional tree simulation applied to 'golden delicious' apple trees Marek Fiser Purdue University

More information

Optimal Control of PDEs

Optimal Control of PDEs Optimal Control of PDEs Suzanne Lenhart University of Tennessee, Knoville Department of Mathematics Lecture1 p.1/36 Outline 1. Idea of diffusion PDE 2. Motivating Eample 3. Big picture of optimal control

More information

" #$ P UTS W U X [ZY \ Z _ `a \ dfe ih j mlk n p q sr t u s q e ps s t x q s y i_z { U U z W } y ~ y x t i e l US T { d ƒ ƒ ƒ j s q e uˆ ps i ˆ p q y

 #$ P UTS W U X [ZY \ Z _ `a \ dfe ih j mlk n p q sr t u s q e ps s t x q s y i_z { U U z W } y ~ y x t i e l US T { d ƒ ƒ ƒ j s q e uˆ ps i ˆ p q y " #$ +. 0. + 4 6 4 : + 4 ; 6 4 < = =@ = = =@ = =@ " #$ P UTS W U X [ZY \ Z _ `a \ dfe ih j mlk n p q sr t u s q e ps s t x q s y i_z { U U z W } y ~ y x t i e l US T { d ƒ ƒ ƒ j s q e uˆ ps i ˆ p q y h

More information

An Introduction to Optimal Control Applied to Disease Models

An Introduction to Optimal Control Applied to Disease Models An Introduction to Optimal Control Applied to Disease Models Suzanne Lenhart University of Tennessee, Knoxville Departments of Mathematics Lecture1 p.1/37 Example Number of cancer cells at time (exponential

More information

$%! & (, -3 / 0 4, 5 6/ 6 +7, 6 8 9/ 5 :/ 5 A BDC EF G H I EJ KL N G H I. ] ^ _ ` _ ^ a b=c o e f p a q i h f i a j k e i l _ ^ m=c n ^

$%! & (, -3 / 0 4, 5 6/ 6 +7, 6 8 9/ 5 :/ 5 A BDC EF G H I EJ KL N G H I. ] ^ _ ` _ ^ a b=c o e f p a q i h f i a j k e i l _ ^ m=c n ^ ! #" $%! & ' ( ) ) (, -. / ( 0 1#2 ' ( ) ) (, -3 / 0 4, 5 6/ 6 7, 6 8 9/ 5 :/ 5 ;=? @ A BDC EF G H I EJ KL M @C N G H I OPQ ;=R F L EI E G H A S T U S V@C N G H IDW G Q G XYU Z A [ H R C \ G ] ^ _ `

More information

ALTER TABLE Employee ADD ( Mname VARCHAR2(20), Birthday DATE );

ALTER TABLE Employee ADD ( Mname VARCHAR2(20), Birthday DATE ); !! "# $ % & '( ) # * +, - # $ "# $ % & '( ) # *.! / 0 "# "1 "& # 2 3 & 4 4 "# $ % & '( ) # *!! "# $ % & # * 1 3 - "# 1 * #! ) & 3 / 5 6 7 8 9 ALTER ; ? @ A B C D E F G H I A = @ A J > K L ; ?

More information

Examination paper for TFY4240 Electromagnetic theory

Examination paper for TFY4240 Electromagnetic theory Department of Physics Examination paper for TFY4240 Electromagnetic theory Academic contact during examination: Associate Professor John Ove Fjærestad Phone: 97 94 00 36 Examination date: 16 December 2015

More information

General Neoclassical Closure Theory: Diagonalizing the Drift Kinetic Operator

General Neoclassical Closure Theory: Diagonalizing the Drift Kinetic Operator General Neoclassical Closure Theory: Diagonalizing the Drift Kinetic Operator E. D. Held eheld@cc.usu.edu Utah State University General Neoclassical Closure Theory:Diagonalizing the Drift Kinetic Operator

More information

A Study on the Analysis of Measurement Errors of Specific Gravity Meter

A Study on the Analysis of Measurement Errors of Specific Gravity Meter HWAHAK KONGHAK Vol. 40, No. 6, December, 2002, pp. 676-680 (2001 7 2, 2002 8 5 ) A Study on the Analysis of Measurement Errors of Specific Gravity Meter Kang-Jin Lee, Jae-Young Her, Young-Cheol Ha, Seung-Hee

More information

A Study on Dental Health Awareness of High School Students

A Study on Dental Health Awareness of High School Students Journal of Dental Hygiene Science Vol. 3, No. 1,. 23~ 31 (2003), 1 Su-Min Yoo and Geum-Sun Ahn 1 Deartment of Dental Hygiene, Dong-u College 1 Deartment of Dental Hygiene, Kyung Bok College In this research,

More information

Max. Input Power (W) Input Current (Arms) Dimming. Enclosure

Max. Input Power (W) Input Current (Arms) Dimming. Enclosure Product Overview XI025100V036NM1M Input Voltage (Vac) Output Power (W) Output Voltage Range (V) Output urrent (A) Efficiency@ Max Load and 70 ase Max ase Temp. ( ) Input urrent (Arms) Max. Input Power

More information

Matrices and Determinants

Matrices and Determinants Matrices and Determinants Teaching-Learning Points A matri is an ordered rectanguar arra (arrangement) of numbers and encosed b capita bracket [ ]. These numbers are caed eements of the matri. Matri is

More information

Relation Between the Growth Twin and the Morphology of a Czochralski Silicon Single Crystal

Relation Between the Growth Twin and the Morphology of a Czochralski Silicon Single Crystal Korean J. Crystallography Vol. 11, No. 4, pp.207~211, 2000 LG, Relation Between the Growth Twin and the Morphology of a Czochralski Silicon Single Crystal Bong Mo Park LG Siltron Inc., 283, Imsoo-dong,

More information

Vector analysis. 1 Scalars and vectors. Fields. Coordinate systems 1. 2 The operator The gradient, divergence, curl, and Laplacian...

Vector analysis. 1 Scalars and vectors. Fields. Coordinate systems 1. 2 The operator The gradient, divergence, curl, and Laplacian... Vector analysis Abstract These notes present some background material on vector analysis. Except for the material related to proving vector identities (including Einstein s summation convention and the

More information

OC330C. Wiring Diagram. Recommended PKH- P35 / P50 GALH PKA- RP35 / RP50. Remarks (Drawing No.) No. Parts No. Parts Name Specifications

OC330C. Wiring Diagram. Recommended PKH- P35 / P50 GALH PKA- RP35 / RP50. Remarks (Drawing No.) No. Parts No. Parts Name Specifications G G " # $ % & " ' ( ) $ * " # $ % & " ( + ) $ * " # C % " ' ( ) $ * C " # C % " ( + ) $ * C D ; E @ F @ 9 = H I J ; @ = : @ A > B ; : K 9 L 9 M N O D K P D N O Q P D R S > T ; U V > = : W X Y J > E ; Z

More information

Constructive Decision Theory

Constructive Decision Theory Constructive Decision Theory Joe Halpern Cornell University Joint work with Larry Blume and David Easley Economics Cornell Constructive Decision Theory p. 1/2 Savage s Approach Savage s approach to decision

More information

The University of Bath School of Management is one of the oldest established management schools in Britain. It enjoys an international reputation for

The University of Bath School of Management is one of the oldest established management schools in Britain. It enjoys an international reputation for The University of Bath School of Management is one of the oldest established management schools in Britain. It enjoys an international reputation for the quality of its teaching and research. Its mission

More information

This document has been prepared by Sunder Kidambi with the blessings of

This document has been prepared by Sunder Kidambi with the blessings of Ö À Ö Ñ Ø Ò Ñ ÒØ Ñ Ý Ò Ñ À Ö Ñ Ò Ú º Ò Ì ÝÊ À Å Ú Ø Å Ê ý Ú ÒØ º ÝÊ Ú Ý Ê Ñ º Å º ² ºÅ ý ý ý ý Ö Ð º Ñ ÒÜ Æ Å Ò Ñ Ú «Ä À ý ý This document has been prepared by Sunder Kidambi with the blessings of Ö º

More information

Front-end. Organization of a Modern Compiler. Middle1. Middle2. Back-end. converted to control flow) Representation

Front-end. Organization of a Modern Compiler. Middle1. Middle2. Back-end. converted to control flow) Representation register allocation instruction selection Code Low-level intermediate Representation Back-end Assembly array references converted into low level operations, loops converted to control flow Middle2 Low-level

More information

Estimation of Retention Factors of Nucleotides by Buffer Concentrations in RP-HPLC

Estimation of Retention Factors of Nucleotides by Buffer Concentrations in RP-HPLC HWAHAK KONGHAK Vol. 38, No. 5, October, 2000, pp. 626-632 (Journal of the Korean Institute of Chemical Engineers) RP-HPLC Nucleotides (2000 2 1, 2000 4 1 ) Estimation of Retention Factors of Nucleotides

More information

QUESTIONS ON QUARKONIUM PRODUCTION IN NUCLEAR COLLISIONS

QUESTIONS ON QUARKONIUM PRODUCTION IN NUCLEAR COLLISIONS International Workshop Quarkonium Working Group QUESTIONS ON QUARKONIUM PRODUCTION IN NUCLEAR COLLISIONS ALBERTO POLLERI TU München and ECT* Trento CERN - November 2002 Outline What do we know for sure?

More information

Plasma diagnostics and abundance determinations for planetary nebulae current status. Xiaowei Liu Department of Astronomy, Peking University

Plasma diagnostics and abundance determinations for planetary nebulae current status. Xiaowei Liu Department of Astronomy, Peking University 3 ' 4 2 - '. %! A?@ @ 3 +.?; = ; %,9 ' ü / :, %4 ' 9 8 +! (76 5 +. *". 34 %, /, /10 *$+,,' -+!. *$+ () ', ' & "$# Plasma diagnostics and abundance determinations for planetary nebulae current status

More information

SCOTT PLUMMER ASHTON ANTONETTI

SCOTT PLUMMER ASHTON ANTONETTI 2742 A E E E, UE, AAAMA 3802 231 EE AEA 38,000-cre dversfed federl cmus 41,000 emloyees wth 72+ dfferent gences UE roosed 80-cre mster-lnned develoment 20 home stes 3,000F of vllgestyle retl 100,000 E

More information

Loop parallelization using compiler analysis

Loop parallelization using compiler analysis Loop parallelization using compiler analysis Which of these loops is parallel? How can we determine this automatically using compiler analysis? Organization of a Modern Compiler Source Program Front-end

More information

Redoing the Foundations of Decision Theory

Redoing the Foundations of Decision Theory Redoing the Foundations of Decision Theory Joe Halpern Cornell University Joint work with Larry Blume and David Easley Economics Cornell Redoing the Foundations of Decision Theory p. 1/21 Decision Making:

More information

!!"# $% &" ( )

!!# $% & ( ) 2002, Vol. 46, No. 6 Printed in the Republic of Korea!!"# $% &" * (2002. 5. 9 ) A Survey of Secondary School Science Teachers Thinking on Classifying Phenomena Related to Dissolution of Ionic Compound

More information

Pharmacological and genomic profiling identifies NF-κB targeted treatment strategies for mantle cell lymphoma

Pharmacological and genomic profiling identifies NF-κB targeted treatment strategies for mantle cell lymphoma CORRECTION NOTICE Nat. Med. 0, 87 9 (014) Pharmacoogica and genomic profiing identifies NF-κB targeted treatment strategies for mante ce ymphoma Rami Raha, Mareie Fric, Rodrigo Romero, Joshua M Korn, Robert

More information

TELEMATICS LINK LEADS

TELEMATICS LINK LEADS EEAICS I EADS UI CD PHOE VOICE AV PREIU I EADS REQ E E A + A + I A + I E B + E + I B + E + I B + E + H B + I D + UI CD PHOE VOICE AV PREIU I EADS REQ D + D + D + I C + C + C + C + I G G + I G + I G + H

More information

Damping Ring Requirements for 3 TeV CLIC

Damping Ring Requirements for 3 TeV CLIC Damping Ring Requirements for 3 TeV CLIC Quantity Symbol Value Bunch population N b 9 4.1 10 No. of bunches/train k bt 154 Repetition frequency f r 100 Hz Horizontal emittance γε x 7 4.5 10 m Vertical

More information

t π ö óœ Ë π l v π [ JA :

t π ö óœ Ë π l v π [ JA : No. of Printed Pages 6 TGS (321) [ 18 HDGPKAC DL2Y(O) ] Diploma in Elementary Education Second Year (Old Course) Exam., 2018 ( D. El. Ed. ) Course Code 14C : Teaching of General Science Full Marks : 80

More information

ETIKA V PROFESII PSYCHOLÓGA

ETIKA V PROFESII PSYCHOLÓGA P r a ž s k á v y s o k á š k o l a p s y c h o s o c i á l n í c h s t u d i í ETIKA V PROFESII PSYCHOLÓGA N a t á l i a S l o b o d n í k o v á v e d ú c i p r á c e : P h D r. M a r t i n S t r o u

More information

T T V e g em D e j ) a S D } a o "m ek j g ed b m "d mq m [ d, )

T T V e g em D e j ) a S D } a o m ek j g ed b m d mq m [ d, ) . ) 6 3 ; 6 ;, G E E W T S W X D ^ L J R Y [ _ ` E ) '" " " -, 7 4-4 4-4 ; ; 7 4 4 4 4 4 ;= : " B C CA BA " ) 3D H E V U T T V e g em D e j ) a S D } a o "m ek j g ed b m "d mq m [ d, ) W X 6 G.. 6 [ X

More information

AN IDENTIFICATION ALGORITHM FOR ARMAX SYSTEMS

AN IDENTIFICATION ALGORITHM FOR ARMAX SYSTEMS AN IDENTIFICATION ALGORITHM FOR ARMAX SYSTEMS First the X, then the AR, finally the MA Jan C. Willems, K.U. Leuven Workshop on Observation and Estimation Ben Gurion University, July 3, 2004 p./2 Joint

More information

The Effect of Deposition Parameter on Electrical Resistivity of TiAlN Thin Film

The Effect of Deposition Parameter on Electrical Resistivity of TiAlN Thin Film HWAHAK KONGHAK Vol. 40, No. 4, August, 00, pp. 59-533 TiAlN Electrical Resistivity * * (00 4 3, 00 7 31 ) The Effect of Deposition Parameter on Electrical Resistivity of TiAlN Thin Film Young Soo Song,

More information

Sample Exam 1: Chapters 1, 2, and 3

Sample Exam 1: Chapters 1, 2, and 3 L L 1 ' ] ^, % ' ) 3 Sample Exam 1: Chapters 1, 2, and 3 #1) Consider the lineartime invariant system represented by Find the system response and its zerostate and zeroinput components What are the response

More information

UNIQUE FJORDS AND THE ROYAL CAPITALS UNIQUE FJORDS & THE NORTH CAPE & UNIQUE NORTHERN CAPITALS

UNIQUE FJORDS AND THE ROYAL CAPITALS UNIQUE FJORDS & THE NORTH CAPE & UNIQUE NORTHERN CAPITALS Q J j,. Y j, q.. Q J & j,. & x x. Q x q. ø. 2019 :. q - j Q J & 11 Y j,.. j,, q j q. : 10 x. 3 x - 1..,,. 1-10 ( ). / 2-10. : 02-06.19-12.06.19 23.06.19-03.07.19 30.06.19-10.07.19 07.07.19-17.07.19 14.07.19-24.07.19

More information

cº " 6 >IJV 5 l i u $

cº  6 >IJV 5 l i u $ !"!#" $ #! &'!!"! (!)*)+), :;23 V' )! *" #$ V ' ' - & +# # J E 1 8# J E.R > +.+# E X78 E.R1 8#[0 FZE > 1 8# 0IJ"U 2A > 1 8# J EK? FZE a2 J+# ;1 8# J EK. C B.> B.> Y $ 1 8# J E. 4 8 B.EK\ X Q8#\ > 1 8#

More information

New BaBar Results on Rare Leptonic B Decays

New BaBar Results on Rare Leptonic B Decays New BaBar Results on Rare Leptonic B Decays Valerie Halyo Stanford Linear Accelerator Center (SLAC) FPCP 22 valerieh@slac.stanford.edu 1 Table of Contents Motivation to look for and Analysis Strategy Measurement

More information

A Functional Quantum Programming Language

A Functional Quantum Programming Language A Functional Quantum Programming Language Thorsten Altenkirch University of Nottingham based on joint work with Jonathan Grattage and discussions with V.P. Belavkin supported by EPSRC grant GR/S30818/01

More information

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 REDCLIFF MUNICIPAL PLANNING COMMISSION FOR COMMENT/DISCUSSION DATE: TOPIC: April 27 th, 2018 Bylaw 1860/2018, proposed amendments to the Land Use Bylaw regarding cannabis

More information

: œ Ö: =? À =ß> real numbers. œ the previous plane with each point translated by : Ðfor example,! is translated to :)

: œ Ö: =? À =ß> real numbers. œ the previous plane with each point translated by : Ðfor example,! is translated to :) â SpanÖ?ß@ œ Ö =? > @ À =ß> real numbers : SpanÖ?ß@ œ Ö: =? > @ À =ß> real numbers œ the previous plane with each point translated by : Ðfor example, is translated to :) á In general: Adding a vector :

More information

Dimethyl Ether Production using a Reactive Distillation Process

Dimethyl Ether Production using a Reactive Distillation Process Korean Chem. Eng. Res., Vol. 42, No. 1, February, 2004, pp. 44-52 305-764 220 (2003 10 1, 2003 12 9 ) Dimethyl Ether Production using a Reactive Distillation Process Younghwa Koo and Myungwan Han Department

More information

PART IV LIVESTOCK, POULTRY AND FISH PRODUCTION

PART IV LIVESTOCK, POULTRY AND FISH PRODUCTION ! " $#%(' ) PART IV LIVSTOCK, POULTRY AND FISH PRODUCTION Table (93) MAIN GROUPS OF ANIMAL PRODUCTS Production 1000 M.T Numbers 1000 Head Type 2012 Numbers Cattle 54164.5 53434.6 Buffaloes 4304.51 4292.51

More information

A Theory of Universal AI

A Theory of Universal AI A Theory of Universa AI Literature Marcus Hutter Kircherr, Li, and Vitanyi Presenter Prashant J. Doshi CS594: Optima Decision Maing A Theory of Universa Artificia Inteigence p.1/18 Roadmap Caim Bacground

More information

ISO/IEC JTC1/SC2/WG2 N2

ISO/IEC JTC1/SC2/WG2 N2 ISO/IEC JTC1/SC2/WG2 N2 2000-04-13 Universal Multiple-Octet Coded Character Set International Organization for Standardization Organisation Internationale de Normalisation Œåæäóíàðîäíàß îðãàíèçàöèß ïî

More information

T i t l e o f t h e w o r k : L a M a r e a Y o k o h a m a. A r t i s t : M a r i a n o P e n s o t t i ( P l a y w r i g h t, D i r e c t o r )

T i t l e o f t h e w o r k : L a M a r e a Y o k o h a m a. A r t i s t : M a r i a n o P e n s o t t i ( P l a y w r i g h t, D i r e c t o r ) v e r. E N G O u t l i n e T i t l e o f t h e w o r k : L a M a r e a Y o k o h a m a A r t i s t : M a r i a n o P e n s o t t i ( P l a y w r i g h t, D i r e c t o r ) C o n t e n t s : T h i s w o

More information

Unit 3. Digital encoding

Unit 3. Digital encoding Unit 3. Digital encoding Digital Electronic Circuits (Circuitos Electrónicos Digitales) E.T.S.I. Informática Universidad de Sevilla 9/2012 Jorge Juan 2010, 2011, 2012 You are free to

More information

4.3 Laplace Transform in Linear System Analysis

4.3 Laplace Transform in Linear System Analysis 4.3 Laplace Transform in Linear System Analysis The main goal in analysis of any dynamic system is to find its response to a given input. The system response in general has two components: zero-state response

More information

DISSIPATIVE SYSTEMS. Lectures by. Jan C. Willems. K.U. Leuven

DISSIPATIVE SYSTEMS. Lectures by. Jan C. Willems. K.U. Leuven DISSIPATIVE SYSTEMS Lectures by Jan C. Willems K.U. Leuven p.1/26 LYAPUNOV FUNCTIONS Consider the classical dynamical system, the flow with, the state, and Denote the set of solutions, the vector-field.

More information

Principal Secretary to Government Haryana, Town & Country Planning Department, Haryana, Chandigarh.

Principal Secretary to Government Haryana, Town & Country Planning Department, Haryana, Chandigarh. 1 From To Principal Secretary to Government Haryana, Town & Country Planning Department, Haryana, Chandigarh. The Director General, Town & Country Planning Department, Haryana, Chandigarh. Memo No. Misc-2339

More information

B œ c " " ã B œ c 8 8. such that substituting these values for the B 3 's will make all the equations true

B œ c   ã B œ c 8 8. such that substituting these values for the B 3 's will make all the equations true System of Linear Equations variables Ð unknowns Ñ B" ß B# ß ÞÞÞ ß B8 Æ Æ Æ + B + B ÞÞÞ + B œ, "" " "# # "8 8 " + B + B ÞÞÞ + B œ, #" " ## # #8 8 # ã + B + B ÞÞÞ + B œ, 3" " 3# # 38 8 3 ã + 7" B" + 7# B#

More information

SOLAR MORTEC INDUSTRIES.

SOLAR MORTEC INDUSTRIES. SOLAR MORTEC INDUSTRIES www.mortecindustries.com.au Wind Regions Region A Callytharra Springs Gascoyne Junction Green Head Kununurra Lord Howe Island Morawa Toowoomba Wittanoom Bourke Region B Adelaide

More information

&i à ƒåi à A t l v π [É A :

&i à ƒåi à A t l v π [É A : No. of Printed Pages 7 (671) [ 18 HDGPKAC DL1Y(N) ] Diploma in Elementary Education First Year (New) Exam., 2018 ( D. El. Ed. ) Course Code 02 : Education, Society and Curriculum Full Marks : 80 Time :

More information

Complex Analysis. PH 503 Course TM. Charudatt Kadolkar Indian Institute of Technology, Guwahati

Complex Analysis. PH 503 Course TM. Charudatt Kadolkar Indian Institute of Technology, Guwahati Complex Analysis PH 503 Course TM Charudatt Kadolkar Indian Institute of Technology, Guwahati ii Copyright 2000 by Charudatt Kadolkar Preface Preface Head These notes were prepared during the lectures

More information

Ú Bruguieres, A. Virelizier, A. [4] Á «Î µà Monoidal

Ú Bruguieres, A. Virelizier, A. [4] Á «Î µà Monoidal 40 2 Æ Vol.40, No.2 2011 4 ADVANCES IN MATHEMATICS April, 2011 273165) T- ÆÖ Ñ Ó 1,, 2 (1. È Ä È 832003; 2. È Ä È Ì. ½ A- (coring) T- (comonad) ( ± A º ¼ T º (monad)).» ³¹ (firm) µ ³ Frobenius ² ¾ ³ ¾

More information

ACS AKK R0125 REV B 3AKK R0125 REV B 3AKK R0125 REV C KR Effective : Asea Brown Boveri Ltd.

ACS AKK R0125 REV B 3AKK R0125 REV B 3AKK R0125 REV C KR Effective : Asea Brown Boveri Ltd. ACS 100 Í ACS 100 Í 3AKK R0125 REV B 3AKK R0125 REV B 3AKK R0125 REV C KR Effective : 1999.9 1999 Asea Brown Boveri Ltd. 2 ! ACS100 { { ä ~.! ACS100 i{ ~. Õ 5 ˆ Ã ACS100 À Ãåä.! ˆ [ U1, V1, W1(L,N), U2,

More information

F O R SOCI AL WORK RESE ARCH

F O R SOCI AL WORK RESE ARCH 7 TH EUROPE AN CONFERENCE F O R SOCI AL WORK RESE ARCH C h a l l e n g e s i n s o c i a l w o r k r e s e a r c h c o n f l i c t s, b a r r i e r s a n d p o s s i b i l i t i e s i n r e l a t i o n

More information

â, Đ (Very Long Baseline Interferometry, VLBI)

â, Đ (Very Long Baseline Interferometry, VLBI) ½ 55 ½ 5 Í Vol.55 No.5 2014 9 ACTA ASTRONOMICA SINICA Sep., 2014» Á Çý è 1,2 1,2 å 1,2 Ü ô 1,2 ï 1,2 ï 1,2 à 1,3 Æ Ö 3 ý (1 Á Í 200030) (2 Á Í û À 210008) (3 541004) ÇÅè 1.5 GHz Á è, î Í, û ÓÆ Å ò ½Ò ¼ï.

More information

February 17, 2015 REQUEST FOR PROPOSALS. For Columbus Metropolitan Library. Issued by: Purchasing Division 96 S. Grant Ave. Columbus, OH 43215

February 17, 2015 REQUEST FOR PROPOSALS. For Columbus Metropolitan Library. Issued by: Purchasing Division 96 S. Grant Ave. Columbus, OH 43215 F 7, 05 RQU FOR PROPOL P/B & O RFP L 5-006 F L : P D 96 G, OH 435 D : 3, 05 N :00 N (, O L ) W D, P P D, F D : (64) 849-034; F: (64) 849-34 @ RQU FOR PROPOL NRUON L ( L L ) R P ( RFP ) P B P N L 5-006

More information

Towards a numerical solution of the "1/2 vs. 3/2" puzzle

Towards a numerical solution of the 1/2 vs. 3/2 puzzle Towards a numerical solution of the /2 s 3/2 puzzle Benoît Blossier DESY Zeuthen Motiations Hea Quark Effectie Theor Theoretical expectations Experimental measurements umerical computation of Conclusion

More information

Symbols and dingbats. A 41 Α a 61 α À K cb ➋ à esc. Á g e7 á esc. Â e e5 â. Ã L cc ➌ ã esc ~ Ä esc : ä esc : Å esc * å esc *

Symbols and dingbats. A 41 Α a 61 α À K cb ➋ à esc. Á g e7 á esc. Â e e5 â. Ã L cc ➌ ã esc ~ Ä esc : ä esc : Å esc * å esc * Note: Although every effort ws tken to get complete nd ccurte tble, the uhtor cn not be held responsible for ny errors. Vrious sources hd to be consulted nd MIF hd to be exmined to get s much informtion

More information

An improved algorithm for scheduling two identical machines with batch delivery consideration

An improved algorithm for scheduling two identical machines with batch delivery consideration 01c $ Ê Æ Æ 117ò 11Ï March, 01 Operations Research Transactions Vol.17 No.1 1$ÑüÓ.ÅüS KU?Ž{ [ 1 4Šz 1, Á ïä 1$ÑüÓ.ÅüS K. T K ó üó.åþ\ó óó d ýnþ z $Ñ r. ùpbó køóônœ 8I žml kó xˆ r Åì žm Ñ ( 14 + ε)-cq 9

More information

Obtain from theory/experiment a value for the absorbtion cross-section. Calculate the number of atoms/ions/molecules giving rise to the line.

Obtain from theory/experiment a value for the absorbtion cross-section. Calculate the number of atoms/ions/molecules giving rise to the line. Line Emission Observations of spectral lines offer the possibility of determining a wealth of information about an astronomical source. A usual plan of attack is :- Identify the line. Obtain from theory/experiment

More information

R for beginners. 2 The few things to know before st. 8 Index 31

R for beginners. 2 The few things to know before st. 8 Index 31 ; & & & 8 * ( 0 " & 9 1 R f Eu l 1 W R? 3 T fw kw f 5 3-4.1 T

More information

Towards a High Level Quantum Programming Language

Towards a High Level Quantum Programming Language MGS Xmas 04 p.1/?? Towards a High Level Quantum Programming Language Thorsten Altenkirch University of Nottingham based on joint work with Jonathan Grattage and discussions with V.P. Belavkin supported

More information

MARKET AREA UPDATE Report as of: 1Q 2Q 3Q 4Q

MARKET AREA UPDATE Report as of: 1Q 2Q 3Q 4Q Year: 2013 Market Area (Cit, State): Greater Portland, OR MARKET AREA UPDATE Report as of: 1Q 2Q 3Q 4Q Provided b (Compan / Companies): Coldwell Banker Seal, Archibald Relocation, Prudential Northwest

More information

Java Applets / Flash Java Applet vs. Flash

Java Applets / Flash Java Applet vs. Flash ava Alet / Flah ava Alet v. Flah oltal oblem wth Mooft hhl otable moe dfflt develomet ot a oblem le o exellet val develomet tool Alet / Flah ood fo tato volv omlex e t whee XTML t elemet ae ot adeqate

More information

New method for solving nonlinear sum of ratios problem based on simplicial bisection

New method for solving nonlinear sum of ratios problem based on simplicial bisection V Ù â ð f 33 3 Vol33, No3 2013 3 Systems Engineering Theory & Practice Mar, 2013 : 1000-6788(2013)03-0742-06 : O2112!"#$%&')(*)+),-))/0)1)23)45 : A 687:9 1, ;:= 2 (1?@ACBEDCFHCFEIJKLCFFM, NCO 453007;

More information

n P! " # $ % & % & ' ( ) * + % $, $ -. $ -..! " # ) & % $/ $ - 0 1 2 3 4 5 6 7 3 8 7 9 9 : 3 ; 1 7 < 9 : 5 = > : 9? @ A B C D E F G HI J G H K D L M N O P Q R S T U V M Q P W X X Y W X X Z [ Y \ ] M

More information

Thermal Conductivity of Electric Molding Composites Filled with β-si 3 N 4

Thermal Conductivity of Electric Molding Composites Filled with β-si 3 N 4 22 Ê 6  ŠVol. 22, No. 6 2007 11 à Journal of Inorganic Materials Nov., 2007 Ð ¹: 1000-324X(200706-1201-05 β-si 3 N 4 / ¾Ú Đ Â ÉÓÅÖ ¼» 1, ³ º 1, µ² 2, ¹ 3 (1. ÅƱ 100084; 2. 100081; 3. ««210016 Û«º β-si

More information

Lower Austria. The Big Travel Map. Big Travel Map of Lower Austria.

Lower Austria. The Big Travel Map. Big Travel Map of Lower Austria. v v v :,000, v v v v, v j, Z ö V v! ö +4/4/000 000 @ : / : v v V, V,,000 v v v v v v 08 V, v j?, v V v v v v v v,000, V v V, v V V vv /Z, v / v,, v v V, v x 6,000 v v 00,000 v, x v U v ( ) j v, x q J J

More information

Executive Committee and Officers ( )

Executive Committee and Officers ( ) Gifted and Talented International V o l u m e 2 4, N u m b e r 2, D e c e m b e r, 2 0 0 9. G i f t e d a n d T a l e n t e d I n t e r n a t i o n a2 l 4 ( 2), D e c e m b e r, 2 0 0 9. 1 T h e W o r

More information

P a g e 5 1 of R e p o r t P B 4 / 0 9

P a g e 5 1 of R e p o r t P B 4 / 0 9 P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e

More information

I N A C O M P L E X W O R L D

I N A C O M P L E X W O R L D IS L A M I C E C O N O M I C S I N A C O M P L E X W O R L D E x p l o r a t i o n s i n A g-b eanste d S i m u l a t i o n S a m i A l-s u w a i l e m 1 4 2 9 H 2 0 0 8 I s l a m i c D e v e l o p m e

More information

Subrings and Ideals 2.1 INTRODUCTION 2.2 SUBRING

Subrings and Ideals 2.1 INTRODUCTION 2.2 SUBRING Subrings and Ideals Chapter 2 2.1 INTRODUCTION In this chapter, we discuss, subrings, sub fields. Ideals and quotient ring. We begin our study by defining a subring. If (R, +, ) is a ring and S is a non-empty

More information

Emphases of Calculus Infinite Sequences and Series Page 1. , then {a n } converges. lim a n = L. form í8 v «à L Hôpital Rule JjZ lim

Emphases of Calculus Infinite Sequences and Series Page 1. , then {a n } converges. lim a n = L. form í8 v «à L Hôpital Rule JjZ lim Emhases o Calculus Ininite Sequences an Series Page 1 Sequences (b) lim = L eists rovie that or any given ε > 0, there eists N N such that L < ε or all n > N ¹, YgM L íï böüÿªjöü, Éb n D bygíí I an { }

More information

Building Products Ltd. G Jf. CIN No. L26922KA199SPLC018990

Building Products Ltd. G Jf. CIN No. L26922KA199SPLC018990 Building Products Ltd.! #$%&'( )*$+.+/'12 3454*67 89 :;= >?? @*;;* ABCDEFGHH @!EJ KLM OGGO RS*4$ST U$+V.+W'X6 $Y Z74' [4%\*67 ]^_ `?a bc>de fg>h> iddjkl mno ApqCDEFrHHHO @ce @sbt?u @vwx yz PD @ Q { }~

More information

THE ANALYSIS OF THE CONVECTIVE-CONDUCTIVE HEAT TRANSFER IN THE BUILDING CONSTRUCTIONS. Zbynek Svoboda

THE ANALYSIS OF THE CONVECTIVE-CONDUCTIVE HEAT TRANSFER IN THE BUILDING CONSTRUCTIONS. Zbynek Svoboda THE NLSIS OF THE CONECTIE-CONDUCTIE HET TRNSFER IN THE BUILDING CONSTRUCTIONS Zbynek Soboda Czech Technical Uniersity in Prague Faculty of Ciil Engineering 166 29 Prague 6 - Czech Republic BSTRCT The numerical

More information

The Periodic Table. Periodic Properties. Can you explain this graph? Valence Electrons. Valence Electrons. Paramagnetism

The Periodic Table. Periodic Properties. Can you explain this graph? Valence Electrons. Valence Electrons. Paramagnetism Periodic Properties Atomic & Ionic Radius Energy Electron Affinity We want to understand the variations in these properties in terms of electron configurations. The Periodic Table Elements in a column

More information

Beloved Script. User s Guide

Beloved Script. User s Guide Beloved Script regular bold & User s Guide op e nt y p e fa q: For information on how to access the swashes and alternates, visit LauraWorthingtonType.com/faqs All operating systems come equipped with

More information

CHAPTER 2 LIMITS AND CONTINUITY

CHAPTER 2 LIMITS AND CONTINUITY CHAPTER LIMITS AND CONTINUITY RATES OF CHANGE AND LIMITS (a) Does not eist As approaches from the right, g() approaches 0 As approaches from the left, g() approaches There is no single number L that all

More information

1.0 Hypothesis Testing

1.0 Hypothesis Testing .0 Hypothesis Testing The Six Steps of Hypothesis Testing Rejecting or Accepting the Null Samples and Data. Parametric Tests for Comparing Two Populations Testing Equality of Population Means (T Test!

More information

1. Allstate Group Critical Illness Claim Form: When filing Critical Illness claim, please be sure to include the following:

1. Allstate Group Critical Illness Claim Form: When filing Critical Illness claim, please be sure to include the following: Dear Policyholder, Per your recent request, enclosed you will find the following forms: 1. Allstate Group Critical Illness Claim Form: When filing Critical Illness claim, please be sure to include the

More information

Ed S MArket. NarROW } ] T O P [ { U S E R S G U I D E. urrrrrrrrrrrv

Ed S MArket. NarROW } ] T O P [ { U S E R S G U I D E. urrrrrrrrrrrv Ed S MArket NarROW Q urrrrrrrrrrrv } ] T O P [ { U S E R S G U I D E QUALITY U op e nt y p e fa q: For information on how to access the swashes and alternates, visit LauraWorthingtonType.com/faqs All operating

More information

Optimization of a parallel 3d-FFT with non-blocking collective operations

Optimization of a parallel 3d-FFT with non-blocking collective operations Optimization of a parallel 3d-FFT with non-blocking collective operations Chair of Computer Architecture Technical University of Chemnitz Département de Physique Théorique et Appliquée Commissariat à l

More information

Lecture 4: Hartree-Fock Theory

Lecture 4: Hartree-Fock Theory Lecture 4: Hartree-Fock Theory One determinant to rule them all, One determinant to find them, One determinant to bring them all and in the darkness bind them Second quantization rehearsal The formalism

More information

LEAD IN DRINKING WATER REPORT

LEAD IN DRINKING WATER REPORT 181 US Hwy 46 Mine Hill, NJ 07803 (908) 654-8068 (800) 783-0567 Fax 908-654-8069 LEAD IN DRINKING WATER REPORT Performed At: Montrose School 356 Clark St., South Orange, NJ 07079 Performed For: South Orange

More information

Element Cube Project (x2)

Element Cube Project (x2) Element Cube Project (x2) Background: As a class, we will construct a three dimensional periodic table by each student selecting two elements in which you will need to create an element cube. Helpful Links

More information

Continuing Education and Workforce Training Course Schedule Winter / Spring 2010

Continuing Education and Workforce Training Course Schedule Winter / Spring 2010 Continuing Education and Workforce Training Course Schedule Winter / Spring 2010 www.southeastmn.edu/training Creating the Solution that Fits! Information Information Registration Registration via our

More information

2016 xó ADVANCES IN MATHEMATICS(CHINA) xxx., 2016

2016 xó ADVANCES IN MATHEMATICS(CHINA) xxx., 2016 µ45 µx ½ Ù Vol.45, No.x 206 xó ADVANCES IN MATHEMATICS(CHINA) xxx., 206 doi: 0.845/sxjz.2050b ²Â» µ ¼ Ulam È ( Ų¼ Ò¼ Ã,,, 747000) : ÉÐ Ì Õ ÎÏÓ, ÊÔ Í - Í Ë 6f(x+y) 6f(x y)+4f(3y) = 3f(x+2y) 3f(x 2y)+9f(2y)

More information

DYNAMIC SAMPLED-DATA OUTPUT REGULATION: A SWITCHING ADAPTIVE APPROACH. HUANG Yaxin 1 LIU Yungang 1 ZHANG Jifeng 2,3

DYNAMIC SAMPLED-DATA OUTPUT REGULATION: A SWITCHING ADAPTIVE APPROACH. HUANG Yaxin 1 LIU Yungang 1 ZHANG Jifeng 2,3 X Ú Æ ê Æ J. Sys. Sci. & Math. Scis. xx xx, x, Ä æ Ñ Ñ N!: ƒ g A { æ! 4 # f Ü V,3. ì À Œ Æ Æ ó Æ, L H 56;. I Æ ê Æ X Ú Æ ï Ä, 9; 3. I Æ Œ Æ ê Æ Æ Æ, 49 Á ï Ä g A æ Ñ Ñ N! K. d u 9 Z 6 é X Ú K w Í Š ^ ±

More information

ADVANCES IN MATHEMATICS(CHINA)

ADVANCES IN MATHEMATICS(CHINA) Æ Ý ¹ ADVANCES IN MATHEMATICS(CHINA) 0 median Đ Ó ( ºÕ ³,, ÓÚ, 330013) doi: 10.11845/sxjz.2012080b : u,v ¹ w G, z ÁÇÉ Ë½ ±, È z À u,v ¹ w Ä median. G À²Ï median, G Î Å Ì ÆÄ median. à ²Ï median µ» ÂÍ, ¾

More information

Connection equations with stream variables are generated in a model when using the # $ % () operator or the & ' %

Connection equations with stream variables are generated in a model when using the # $ % () operator or the & ' % 7 9 9 7 The two basic variable types in a connector potential (or across) variable and flow (or through) variable are not sufficient to describe in a numerically sound way the bi-directional flow of matter

More information